Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 67/90,32/45,46/77,663/15
Formula to find GCF of Fractions is
GCF = GCF of Numerators/LCM of Denominators
As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators
In the given fractions GCF of Numerators means GCF of 67,32,46,663
Greatest Common Factor of Numerators i.e. GCF of 67,32,46,663 is 1 .
LCM of Denominators means LCM of 90,45,77,15 as per the given fractions.
LCM of 90,45,77,15 is 6930 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 67,32,46,663
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 67
List of positive integer factors of 67 that divides 67 without a remainder.
1,67
Factors of 32
List of positive integer factors of 32 that divides 32 without a remainder.
1,2,4,8,16,32
Factors of 46
List of positive integer factors of 46 that divides 46 without a remainder.
1,2,23,46
Factors of 663
List of positive integer factors of 663 that divides 663 without a remainder.
1,3,13,17,39,51,221,663
Greatest Common Factor
We found the factors 67,32,46,663 . The biggest common factor number is the GCF number.
So the greatest common factor 67,32,46,663 is 1.
Lets's calculate LCM of 90,45,77,15
3 | 90, 45, 77, 15 |
3 | 30, 15, 77, 5 |
5 | 10, 5, 77, 5 |
2, 1, 77, 1 |
∴ So the LCM of the given numbers is 3 x 3 x 5 x 2 x 1 x 77 x 1 = 6930
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6930
Therefore, the GCF of Fractions 67/90,32/45,46/77,663/15 is 1/6930
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 90,45,77,15 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(90,45,77,15) = 1
common factors(in case of two or more numbers have common factors) = 675
GCF(90,45,77,15) x common factors =1 x 675 = 675
LCM(90,45,77,15) = ( 90 × 45 × 77 × 15 ) / 675
LCM(90,45,77,15) = 4677750 / 675
LCM(90,45,77,15) = 6930
Here are some samples of GCF of Fractions calculations.
Here are some samples of GCF of Fractions calculations.
1. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
2. What is the GCF of Fractions for 67/90, 32/45, 46/77, 663/15?
Answer: GCF of Numerators as per given numbers 67/90, 32/45, 46/77, 663/15 is
GCF of Numerators i.e. for 67,32,46,663 is 1
LCM of denominators i.e. for 90,45,77,15 is 6930.
Thus, GCF of Fractions is 1/6930.Finally, GCF of Fractions for 67/90, 32/45, 46/77, 663/15 is 1/6930.